Inscribed Triangles in Inscribed Circles
A circle in inscribed within an equilateral triangle, and another equilateral triangle is inscribed within the circle.
How much larger is the outside triangle's area than the inside triangle's?
Four times as large.
This is easier to see if you turn the inner triangle upside down.
The area of a square inscribed within a circle inscribed within a square is 1/2.
The area of a hexagon inscribed within a circle inscribed within a hexagon is 3/4.
